@Article{NMTMA-6-637,
author = {Yanping Chen and Tianliang Hou},
title = {Error Estimates and Superconvergence of RT0 Mixed Methods for a Class of Semilinear Elliptic Optimal Control Problems},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2013},
volume = {6},
number = {4},
pages = {637--656},
abstract = {<p style="text-align: justify;">In this paper, we will investigate the error estimates and the
superconvergence property of mixed finite element methods for a
semilinear elliptic control problem with an integral constraint on
control. The state and co-state are approximated by the lowest order
Raviart-Thomas mixed finite element and the control variable
is approximated by piecewise constant functions. We derive some
superconvergence properties for the control variable and the state
variables. Moreover, we derive $L^∞$- and $H^{-1}$-error
estimates both for the control variable and the state variables.
Finally, a numerical example is given to demonstrate the theoretical
results.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2013.1230nm},
url = {http://global-sci.org/intro/article_detail/nmtma/5923.html}
}